Save Score: 0 of 1 pt 6 of 8(1 complete) HW Score: 12.5%, 1 of 8 p 5.5.27 E Ques

Question

Save Score: 0 of 1 pt 6 of 8(1 complete) HW Score: 12.5%, 1 of 8 p 5.5.27 E Question Help Suppose that four successive terms of the Fibonacci sequence are chosen Multiply the first and fourth. Double the product of the second and third. Add the squares of the second and third. The three results obtained form a Pythagorean triple. Find the Pythagorean triple obtained this way using the four given successive terms of the Fibonacci sequence 21. 34,55, 89 The three numbers of the Pythagorean triple are Use a comma to separate answers, but do not use commas in any individual numbers)

Explanation / Answer

Given Fibonacci sequence:

21, 34, 55, 89

by the given data

Multiply the first and fourth : 21(89) = 1869

Double the product of the second and third: 2(34*55) = 2(1870) = 3740

Add the squares of the second and third = (34)2 + (55)2 = 4181

Therefor the three results are 1869, 3740, 4181

Check if these are Pythagorean triple are not

From the Pythgorean triple:

a2 + b2 = c2

(1869)2 + (3740)2 = (3493161) + (13987600) = 17480761 = (4181)2

Therefore

the three numbers of the Pythagorean triple are: 1869, 3740, 4181

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